Not signed in (Sign In)

Start a new discussion

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Discussion Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMar 10th 2016
    • (edited Mar 10th 2016)

    started a minimum at Bousfield-Friedlander theorem

    (the model category theoretic incarnation of idempotent \infty-monads)

    cross-linked with brief paragraphs to Bousfield-Friedlander model structure

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMar 10th 2016
    • (edited Mar 10th 2016)

    I have spelled out the proof of the existence of the model structure at Bousfield-Friedlander theorem – except for the proof of the lemma labeled A.8 (iii) in Bousfield-Friedlander; but for that I at least added a pointer to Goerss-Jardine chapter X, lemma 4.4, where full details are given.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 26th 2016

    I have typed out the remaining proof of the second lemma that enters the proof of the Bousfield-Friedlander theorem.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeMay 26th 2016

    I have typed out the proof of the proposition (here) that in a Bousfield-Friedlander-type Bousfield localization, the fibrations are precisely the “homotopy QQ-modal morphisms”, so to say.

    I directly followed the proof of Goerss-Jardine’s theorem X.4.8, just trying to make it a little more transparent.

    For completeness, we should somewhere have direct proof of all the properties of “naive homotopy pullbacks” that are being invoked. Notably preservation under retracts. Maybe I’ll write that out later.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJun 6th 2016
    • (edited Jun 6th 2016)

    I have expanded the second part of the proof of the proposition (here) which characterizes the fibrations in the QQ-model structure.

    The previous version had been a bit quick towards the end. (In Goerss-Jardine it is done even quicker, but here it is good to actually spell it out.)

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)